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Hooke’s law and spring calculations

Use force and extension, find spring constants and elastic energy, and interpret force–extension data.

Practise

Length and extension

A spring is 19 cm long unloaded and 24 cm long under a 4 N force. The spring obeys Hooke’s law over this range. Find the spring constant. Give your answer to 3 significant figures.

Unloaded length 19 cmLoaded length 24 cmForce 4 N
Spring unloaded length 19 cm; loaded length 24 cm; applied force 4 N. The sketch shows arrangement, not a ruler reading.
Larger diagram
Unloaded length 19 cmLoaded length 24 cmForce 4 N

Treat the given values as exact unless an uncertainty is stated.

Use decimals or e notation, e.g. 4.2e-3. Enter the unit separately.

Hint

Extension is loaded length minus unloaded length.

Worked solution
  1. x = 24 − 19 = 5 cm = 0.05 m.
  2. k = 4 / 0.05 N m⁻¹.
  3. Answer: 80.0 N m⁻¹ (3 significant figures).
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Question type: Length and extension
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Foundation and Higher: this set covers content common to both tiers. Some calculations need several steps.

Force and extension

Extension is the change from unloaded length, measured in metres for F = kx. The force–extension gradient is k when force is vertical and extension horizontal. E = ½kx² applies over the Hooke’s-law range. The limit of proportionality and elastic limit are different: a curved relationship does not by itself prove permanent deformation.

Work through the practical method and sample results

GCSE scope

AQA 8463: 4.5.3; required practical 6 (selected); OCR Gateway J249: P2.3b–e; PM2.3i–iii; PAG P2 (selected). Tasks cover the selected skills listed above.

AQA specification · OCR Gateway specification

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